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Q2r+Q2ras A Universal Billiard

Author

Listed:
  • PATRICIO CORDERO

    (Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas, Departamento de Física, Casilla 2777, Santiago, Chile)

  • ERIC GOLES

    (Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática, Casilla 170, Correo 3, Santiago, Chile)

  • GONZALO HERNANDEZ

    (Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática, Casilla 170, Correo 3, Santiago, Chile)

Abstract

In this work we study the computing capabilities as well as some dynamical properties of an automaton called M4R. This automaton corresponds to the mixing of the energy profiles of two independent copies of the Q2R automaton with frustrations. We associate to each copy of a Q2R an equivalent automaton M2R, which, with the Margoluos neighborhood, exhibits the local changes of the Q2R energy.1By doing so we generalize the dynamics by upgrading M2R according to four partitions of the lattice. This new dynamics — called M4R — is based on a local rule which corresponds to the local energy change of two independent copies of Q2R.The M4R model is reversible and conservative (magnetization is constant in time) and it has properties of a discrete billiard (as some of the hydrodynamics discrete versions of Navier-Stokes models).Moreover, this automaton has powerful computing capabilities. In fact, by using some special configurations of M4R, we exhibit universal gates and register that allow us to code any algorithm.

Suggested Citation

  • Patricio Cordero & Eric Goles & Gonzalo Hernandez, 1992. "Q2r+Q2ras A Universal Billiard," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 251-266.
    • Handle: RePEc:wsi:ijmpcx:v:03:y:1992:i:02:n:s012918319200021x
    DOI: 10.1142/S012918319200021X
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